Solve r^3- 5r^2- 100r^500

Question

Simplify the expression

r^{3} - 5 r^{2}

Evaluate

r^{3} - 5 r^{2} - 100 r^{5} \times 0

Any expression multiplied by 0 equals 0

r^{3} - 5 r^{2} - 0

Solution

r^{3} - 5 r^{2}

Show Solution

r^{2} (r - 5)

Evaluate

r^{3} - 5 r^{2} - 100 r^{5} \times 0

Multiply

More Steps

Multiply the terms

100 r^{5} \times 0

Any expression multiplied by 0 equals 0

0 \times r^{5}

Any expression multiplied by 0 equals 0

0

r^{3} - 5 r^{2} - 0

Removing 0 doesn't change the value,so remove it from the expression

r^{3} - 5 r^{2}

Rewrite the expression

r^{2} \times r - r^{2} \times 5

Solution

r^{2} (r - 5)

Show Solution

r_{1} = 0, r_{2} = 5

Evaluate

r^{3} - 5 r^{2} - 100 r^{5} \times 0

To find the roots of the expression,set the expression equal to 0

r^{3} - 5 r^{2} - 100 r^{5} \times 0 = 0

Multiply

More Steps

Multiply the terms

100 r^{5} \times 0

Any expression multiplied by 0 equals 0

0 \times r^{5}

Any expression multiplied by 0 equals 0

0

r^{3} - 5 r^{2} - 0 = 0

Removing 0 doesn't change the value,so remove it from the expression

r^{3} - 5 r^{2} = 0

Factor the expression

r^{2} (r - 5) = 0

Separate the equation into 2 possible cases

r^{2} = 0 r - 5 = 0

The only way a power can be 0 is when the base equals 0

r = 0 r - 5 = 0

Solve the equation

More Steps

Evaluate

r - 5 = 0

Move the constant to the right-hand side and change its sign

r = 0 + 5

Removing 0 doesn't change the value,so remove it from the expression

r = 5

r = 0 r = 5

Solution

r_{1} = 0, r_{2} = 5

Show Solution